High-accuracy pattern shape evaluating method and apparatus

ABSTRACT

A quantity (or dispersion value) of a distribution of edge position due to random noise is expected to be reduced statistically to 1/N when N edge position data items are averaged. Using this property, the single page image is averaged in a vertical direction with various values of parameter S, and then the edge roughness index is calculated. The S-dependence of the edge roughness index is analyzed and a term of a dispersion value directly proportional to 1/S is determined as being due to noise.

INCORPORATION BY REFERENCE

The present application claims priorities from Japanese applicationsJP2005-000029 filed on Jan. 4, 2005, JP2005-343047 filed on Nov. 29,2005, the contents of which are hereby incorporated by reference intothis application.

BACKGROUND OF THE INVENTION

The present invention relates to fine pattern examining methods andapparatus using detailed shape or size measurement based onnon-destructive observation and image processing, with a scanningmicroscope and methods of evaluating the examining apparatus.

In semiconductor and other industries, evaluation of fine roughness ofrandomly occurring pattern edges called edge roughness has been requiredas the pattern processing sizes become finer. Especially, insemiconductor process it has been known that a local fluctuation of aline width or line width roughness occurring from a (line) edgeroughness or a line's right and left edge roughness of a gate orinterconnect pattern will greatly influence the device performance.Thus, even in the pattern shape evaluation of the semiconductor process,the line-edge or line width roughness need be measured with highaccuracy.

In order to measure the line-edge or line width roughness, however, aset of points representing a pattern edge need be obtained from anobservation image displayed on a scanning electron microscope. Randomnoise occurring in the image acquirement will greatly influence thiswork. As will be described later in more detail, the influence of therandom noise will appear as a bias quantity of the roughness index. Ameasured value of the roughness will be greater than that obtained fromthe shape of a real observation pattern.

The bias quantity has been a question in recent years under thefollowing circumstances although it does not come into question when thereal roughness value is much greater than the bias quantity. First,damage to a specimen or changes in the dimensions of the specimen (dueto pattern shrinkage, charging, adhesion of organic molecules, etc.) dueto irradiation of the specimen with an electron beam can be a problem.In order to prevent this damage or size changes, the observation shouldbe made with as small a dose of electron beam irradiation as possible.If the dose of electron beam irradiation is less, however, the ratio instrength of signal to noise (S/N ratio) becomes smaller. Second, thereare demands for observation of only higher frequency components of theroughness. When the higher frequency components of the roughness areobserved, or a high frequency roughness or short-period roughness isobserved, the roughness will be measured on a short line. Then, since nolonger-period components are measured, the roughness will be measured ona short line. As a result, the roughness value itself will be smaller.In contrast, since the roughness bias quantity due to noise is afluctuation quantity per edge point, the bias quantity will not becomesmaller even when the measured line length is reduced. In other words,if the roughness in the high frequency area is intended to be measured,the bias due to noise will increase relatively. Under thesecircumstances, it is necessary to eliminate the influence of randomnoise from the obtained measured value, and calculate a value of thereal roughness of the observation pattern.

Simultaneously, there are demands for quantifying noise itself for thepurpose of evaluating the performance of the measuring instrument.

In summary, it is necessary to separately take a quantity of roughnessand the influence of noise actually present in the observation patternpresent in the observation pattern from the index of the edge roughnessobserved usually.

In the following, a method of generally calculating the index ofline-edge or line width roughness, the influence of random noise on thevalue of the calculated index value, and a conventional method ofseparating the index value and the random noise will be described.

The edge of a line pattern is calculated as follows. First, the patternis observed from above with the scanning electron microscope. Let ydirection be the direction of a line in a two-dimensional signalintensity distribution obtained and let x direction be the directionperpendicular to the direction of the line. An x-direction distributionof the signal intensity with y as a constant is referred to as a profileof the signal intensity. Such profiles are arranged at constantintervals in the y-direction. When a y-coordinate is specified, acorresponding profile is determined uniquely. FIG. 1 shows arelationship in correspondence between profile and actual patterncross-sectional view. An upper sub-view of FIG. 1 illustrates a profileactually obtained and a lower part of FIG. 1 shows a cross-sectionalview of a line pattern corresponding to the profile. The edge of a linepattern corresponds to a peak of the profile. When an edge roughness isanalyzed, edge points are defined according to a given algorism on theprofile obtained by actual measurement. Thus, the edge point definedaccording to the algorism can not necessarily coincide with a peakappearing on the profile. When a value is specified (and referred to asi) on the y-coordinate is specified, an x-coordinate of a pointcorresponding to the edge can be calculated for the correspondingprofile. Then, y-coordinates can be specified at constant intervals andthen pattern edges can be extracted one after another from thecorresponding profiles, thereby obtaining series data of the patternedge. FIG. 2 schematically illustrates an enlarged view of a part of aline pattern observed on a SEM image. FIG. 2 illustrates obtainingseries data Δx_(i); Δx₁, Δx₂, . . . each indicative of a differencebetween a straight line approximating series data of an edge and arespective one of actual pattern edge positions. The approximatestraight-line comprises a set of averaged values of the edge points, andΔx_(i) corresponds to a deviation of an edge point in a specifiedprofile from the averaged value. FIG. 3 comprises a FIG. 2 viewed inperspective. The width of the line pattern is represented by an intervalbetween right and left approximate straight-lines. A (local) line widthon a specified profile is represented by a series difference w_(i) (=w₁,w₂, . . . ) between the right and left edge series.

Indexes representing degrees of line-edge roughness and line widthroughness will be described together as a roughness index in thefollowing. As roughness indexes, (Δx₁, Δx₂, . . . ) or (w₁, w₂, . . . )is regarded as a set of data and a standard deviation obtained fromthese data values or three times the standard deviation is generallyused. Even at present, these indexes are used in the resist materialsand in the screening of a process. In addition, in the future, it isconsidered that even in the dimension check of the mass productionprocess not only the conventional simple averaged line width or theline's CD (Critical Dimension) but also the roughness indexes need bechecked. At this time, an index of the line-edge or line width roughnessneed be calculated with high accuracy. As shown by non-patent literature1 shown later, the performance of a transistor is predictable from thevalues of the indexes of the line width roughness, but also in thiscase, a high-accuracy width roughness need be obtained.

Proc. SPIE 5375 (2000), pp 468–476 discloses a technique for settingmeasurement parameters comprising an extent of a measurement area in theroughness measurement and that of an interval at which the edge point issampled, based on a spatial frequency distribution of roughness. Inaddition to these measurement parameters, the device performance andmore particularly an extent of noise influence the measured values ofthe actual roughness indexes. Proc. SPIE 5375 (2004), pp 515–533 shownlater discloses a view that the positions of the edge points which willbe observed on each profile have a distribution round a real edge point.Such distribution is considered as arising from noise. Let σ_(e) be adistribution (or standard deviation) of the observed edge pointpositions around the actual position. Then, an edge roughness indexσ_(m) observed is given byσ_(m)=√{square root over (σ₀ ²+σ_(e) ²)}  Ex. 1where σ₀ is the actual edge roughness index (represented by a standarddeviation).

That is, the observed value of the edge roughness index is larger thanthe real value. In the present description text, a change of the edgeroughness index from its real value is referred to as a bias of the edgeroughness. Occurrence of the bias is mainly due to noise.

Similarly, this applies when an object is not edge roughness, but linewidth roughness. In the case of the line width roughness, observedvariation in the positions of the right and left edge points adds tothat of the local line widths and the observed value of the line widthroughness index is larger than the real value. In the following, theedge roughness will be mainly discussed.

Even when a bias is present in the observed value of the edge roughness,the edge roughness index still represents the feature of the patternshape. When σ₀ becomes smaller, σ_(m) becomes rather closer to σ_(e),and does not represent an extent of the edge roughness correctly. When apattern of small line-edge roughness is measured, it is necessary toeliminate the influence of the edge roughness bias and obtain as close avalue to the real index value σ₀ as possible. Even when an index (suchas, for example, a deviation average) other than the above example (orstandard deviation) is used as that of the line-edge or line widthroughness, the observed value will likewise have a bias that reflectsnoise. In the present invention, standard deviation will be used as anindex of roughness in every case for purposes of easy understanding.

Proc. SPIE 5375 (2004), pp 515–533 discloses a method of separating areal value σ₀ and a term σ_(e) due to noise from a measured value σ_(m)of expression 1. In this method, an object pattern is observed aplurality of times, thereby obtaining a plurality of imagescorresponding to two-dimensional signal intensity distributions. Then,all these data are added up (more particularly, the two-dimensionalintensity distributions are either added or averaged) and edge pointpositions are obtained which considered to be close to the real edgepoint positions (referred to as averaged edge points temporarily) fromthe obtained added-up data. The edge point positions obtained byobservation from data for a plurality of pages of data are distributedaround the averaged edge point. A standard deviation of thisdistribution is then calculated and represented by σ_(e).

As described above, since the line-edge or line width roughnessinfluences the characteristics of a semiconductor device, the value ofthe line-edge or line width roughness can be used as a criterion fordetermining whether the semiconductor manufacturing process is good ornot. Thus, in order to evaluate the process, it is necessary tocalculate a real roughness index value representing the line-edge orline width roughness minus a change quantity due to noise. A bias due tonoise included in the line-edge or line width roughness involvesreproducibility of evaluation of a semiconductor evaluation device,namely, a degree of a distribution of the measured values of parametersfor the purpose of evaluation. Thus, in order to evaluate thesemiconductor evaluation device, a distribution of the edge pointpositions itself due to noise need be evaluated.

The problem with the method disclosed in non-patent literature 2 is thatfirst, the method is very time consuming. First, two sets or more ofimage data of the same visual field must be acquired. According tonon-patent literature 2, the image data need be processed statistically,and at least two sets of image data is required. In addition, in orderto obtain a result of high reliability, measurement must be made atleast five positions empirically. Since the image data need be added inthe same visual field, position deviations contained in the image datashould be corrected. When image data is acquired using the scanningelectron microscope, the position of an examination specimen can deviatefrom the visual field of the image due to thermal vibration of thespecimen or a drift of the stage. Correction of the position deviationis time consuming and requires the operator's experience and dataprocessing is complicated. In addition, automation is difficult. Asecond problem is to damage to the specimen. In order to acquire data ona plurality of images, it is necessary to irradiate the specimenrepeatedly with an electron beam (EB). Even when a beam irradiation timeper unit image pickup operation is short, the whole EB radiationquantity increases by repeated irradiation.

As described above, the conventional method of calculating a biascomponent included in the line-edge or line width roughness needs twosets or more of image data and takes a long time for data processing. Inaddition, data analysis that requires skill need be made as a preprocessfor the image data processing. Furthermore, the beam irradiation timefor the specimen increases, thereby damaging the observation patternpossibly.

The problem to be solved by the present invention is to provide a methodand apparatus for evaluating an index of line-edge or line widthroughness present actually in an object to be observed, and a roughnesscomponent due to noise contained in a result of the observation from apiece of image obtained in a usual pattern observation, in a shortertime than in the past without losing substantially the same accuracy asin the conventional method.

SUMMARY OF THE INVENTION

Main five solving means for above-mentioned problems are disclosedherein and divided into two groups: ones using and not using Fourier'stransform. In the following, their principles will be explained and anyof the solving means described below uses any one of a change in aspectrum and a change in the level of random noise due to imageaveraging. In the following description, a standard deviation is usedalways as a roughness index. For simplifying purposes, line-edgeroughness will be described and a similar method may apply to the linewidth roughness.

There is a theorem concerning a signal changing with time that thesignal intensity per unit time is equal to integration of a powerspectrum concerned. Applying this to the line-edge or line widthroughness, it will be known that the square of standard deviation σ isequal to integration of the power spectrum of the roughness. In thefollowing, the principle of the present invention will be describedbased on this property.

(1) First Method:

The first method uses a property that the power spectral density ofline-edge or line width roughness in high-frequency region isproportional to f⁻² where f is spatial frequency. In the function ofpower spectrum density distribution obtained directly from the originaldata provides a distribution in which the frequency characteristic ofthe high frequency area is not directly proportional to f⁻² becausenoise is included. In this case, averaging the original data will leadto reduction of the noise effect on the measured roughness. The effectof noise reduction increases as the number of averaging operationsincreases. For example, by performing the averaging operations anappropriate number of times, the power spectrum density distribution inthe high frequency area will be directly proportional to f⁻². Thus, thepoint of the first method is that by increasing the number of averagingoperations on one set of image data as the original data until thefrequency (f) dependence of the power spectrum density in the highfrequency area shows f⁻² property, the real spectrum component containedin the actually measured data is presumed, which is the point of thefirst method and will be described below in detail.

First, a relationship between edge roughness index to be acquired,averaged edge roughness index and free spectrum of the edge roughness(or power spectrum obtained by Fourier's transform of edge series data)will be described. For simplifying purposes, a unified unit of length tobe used is nm. A direction extending along the line pattern is definedas a vertical or y-direction of the image, and a direction perpendicularto the vertical direction is defined as a horizontal or x-direction.

Observation data obtained by the microscope is made up of signalintensity profiles corresponding in number to the number of scanninglines. Each profile is an x-direction dependence of the detectedsecondary (or reflected) electron signal intensity in the microscopewhen the y-coordinate is fixed. The signal intensity I (x, y) ofobservation data (or subjected to no image processing) where thetwo-dimensional signal intensity distribution is composed of x_(max) andy_(max) data items in x and y directions, respectively, is given byI=f(x,y)  Ex. 2where x is the value of an integer in a range of 1 through x_(max) and yis the value of an integer in a range of 1 through y_(max). Before imageprocessing such as averaging, the profile comprises a function of xwhere y is regarded as a constant in Ex 2.

When the y-direction averaging process that is one of the simplest noisereducing processes is performed on the secondary electron intensitydistribution, a resulting signal intensity is given by

$\begin{matrix}{I = {{f^{\prime}\left( {x,y} \right)} = {\frac{1}{S}{\sum\limits_{j = {y - a}}^{y + b}{f\left( {x,j} \right)}}}}} & {{Ex}.\mspace{14mu} 3}\end{matrix}$where S is the number of times of averaging parameters or operations, aand b each are (S−1)/2 when S is an odd number. When S is an evennumber, a=S/2, b=a−1 or b=S/2, and a=b−1. S=1 corresponds to performingno averaging process.

As will be known from Ex. 3, an averaged profile is obtained byaveraging S unaveraged profiles. Thus, it is expected that the power ofnoise on the profile is reduced greatly, or to approximately 1/S,compared to that present when the profile was not averaged.

Thus, a basic method is deduced which when a roughness index iscalculated, an operator who processes image data visually confirms aFourier's spectrum averaged with parameter S while selecting a Fourier'sspectrum averaged an appropriate number of times. The operator isrequired to increase the value of S until the noise of the spectrumdecreases and the power spectrum density of a relatively high frequencyarea becomes directly proportional to f⁻², at which time the operatorprovides a roughness index using the value of S.

FIG. 4 illustrates a relationship between a spectrum including noise anda real spectrum. The both vertical and horizontal axes of the graph arein logarithmic scale. The slope of the power spectral density shown inFIG. 4 changes at a certain spatial frequency denoted as f₀. Thespectral density is directly proportional to spatial frequency f⁻² in ahigher frequency area than f₀. While this property has been observed inline patterns of various resists and said to be empirically correct, thephysical or chemical meaning of f₀ has not yet been clarified.Approximately the position of f₀ is shown in FIG. 4. While in the realspectrum the f⁻² characteristic of the high frequency area appears,noise components such as shown dotted are superimposed on a spectrumobtained from observation data that has not been subjected to any imageprocessing and the f⁻² characteristic is unclear. By increasing thevalue of the averaging parameter S, the superposed noise is restrictedand a resulting spectrum changes from one with noise shown in FIG. 4 toa real spectrum, or the dotted area decreases.

In order to determine the end point of S without the operator's hand, aproperty is used in which the effect of noise elimination will besaturated when the number of averaging operations increases beyond acertain value. For example, if an algorithm is used which when adifference between the power spectral densities obtained in S and S+1averaging operations is smaller than a certain threshold, determinesthat S or S+1 has reached the end of S, the end of S can be determinedautomatically. The power spectral density after the averaging operationsof number S is calculated, thereby obtaining σ_(m). More specifically,it is required that a frequency band of roughness that the operatordesires to obtain is determined; the power spectral density after theaveraging operations of number S is integrated in the frequency band;and then its square root is calculated.

Let σ₀ be a value obtained. Then, if σ_(e) is calculated based on Ex. 1from σ₀ and σ_(m) obtained from the power spectral density acquiredwithout being subjected the averaging operations, σ_(e) is an indexrepresenting an extent of noise present when no averaging operations areperformed. In the following σ_(m) of Ex. 1 is regarded as a function ofaveraging parameter S as required and notated as σ_(m) (S). For example,σ_(e) (1) represents σ_(e) obtained when S=1 or when no averagingoperations are performed.

(2) Second Method

There is a problem with the first method that information on roughnessof a short period in the y direction, or fine roughness along the edgeof the line pattern, may disappear due to averaging. FIG. 5 shows thepower spectral densities of the measured roughness data before and afterthe averaging operations. The both vertical and horizontal axes of thegraph are in logarithmic scale. Let Δy be an interval of electron beamscanning. Then, as the averaging parameter increase, the power spectrumof the roughness changes as shown in FIG. 5. Noise is superimposed on ahigh frequency area of the spectrum when no averaging operations areperformed on the data. When the data is averaged with averagingparameter S, a roughness whose period is shorter than SΔy will beleveled out and then disappear. This influence will also be exerted oncomponents having a longer period than SΔy and as a result, theintensities of components having a period shorter than 2SΔy will bereduced greatly. This can be easily confirmed by averaging a sinusoidalwaveform having a period T. As a result, noise components is reduced inthe spectrum obtained after the averaging operations and simultaneouslythe power spectrum intensity is greatly reduced in an area where thefrequency is higher than 1/(2SΔy).

In order to obtain a real edge roughness index, the following should bemade: First, a spectrum materially free from noise is obtained byaveraging the original image data sufficiently (for example, a spectrumobtained after the averaging operations shown of the FIG. 5 graph).However, in this spectrum, a signal in a high frequency area wheref≧1/(2SΔy) is not correct). In determining a value of the averagingparameter S for a sufficient averaging operation, the first method maybe used. The frequency-dependence of a power spectrum in the highfrequency area where the spatial frequency f is f≧1/(2SΔy) is predictedor extrapolated based on the shape of a spectrum of a part of an areaclose to the high frequency area where the spatial frequency f isf<1/(2SΔy). The following expression is used for a fitting curve to beused for extrapolation:PSD(f)=A/f ²  Ex. 4where f is the spatial frequency, and A is a proportional constant. Thatis, there is a property that the power spectral density (directlyproportional to the square of a Fourier's amplitude) is inverselyproportional to the square of the spatial frequency in the highfrequency area. Data to be used for extrapolation purposes should betaken from a low frequency area where the spatial frequency f<1/(2SΔy)on the right side of a boundary point appearing in the power spectrum.That is, the operator specifies a frequency f₁ equal to, or higher than,f₀ and extrapolates, using averaged power spectrum data present betweenf₁ and f=1/(2SΔy).

FIG. 6 shows a graph of power spectrum density in which data in the highfrequency area is compensated for by extrapolation. Both the verticaland horizontal axes of FIG. 6 are in logarithmic scale as same as inFIG. 4. In the graph of FIG. 6, a spectrum approximating to the realspectrum compared to the graph of FIG. 5 is obtained. In thisapproximating spectrum, a low frequency area for f<1/(2SΔy) indicates aspectrum obtained after the image data is averaged while a highfrequency area for f≧1/(2SΔy) indicates predicted values.

In order to calculate a noise component quantity using the secondmethod, a required frequency area band (or a hatched part+a dotted partof FIG. 6) is integrated on the spectrum of FIG. 6. The integrated valuecan be regarded as the square of σ₀.

As described above, the second solving method comprises calculating thehatched part of FIG. 6 by approximating a spectrum of the actuallymeasured data, thereby calculating σ₀. Like the first solving method, aninfluence σ_(e) (1) of noise can be calculated if σ₀ is known.

(3) Third Method

There are three problems with each of the first and second methods asfollows. First, the operator must determine a value of a averagingparameter to sufficiently reduce noise. To this end, the operator needsskill. In order to achieve automation, examples of analysis of spectraobtained under various materials and conditions of observation must beformed as a database, which is presumed to be time consuming. A secondproblem is that data processing in Fourier's transform and analysis of aspectrum shape is time consuming. A third problem is that 2^(n) dataitems are needed to perform Fourier's transform at high speeds. If thenumber of data items is not equal to 2^(n), edge series data in aspecified area must be interpolated/extrapolated so as to be 2^(n) dataitems, which is also time consuming. Thus, such calculation would invitean increase in the calculation time and hence the examination time aswell as an increase in the capacity of memory. If software that performssuch a complicated analysis is set on the examination device, a largepart of the storage area of the device would be occupied, therebyimposing restrictions to other functions.

In summary, it is desirable that the calculations described concerningthe first and second solving methods can be implemented easily (orwithout performing Fourier's transform if possible) on a CD-SEM.

In third, fourth and fifth methods to be described below, σ₀ iscalculated using a statistic property that the intensity of random noiseis reduced to 1/S by averaging. When σ₀ is calculated, an index σ_(e)(1) of noise in the device that is not dependent on the averagingparameter can also be calculated.

For simplifying purposes, let L and Δy be the length of an examinationarea and an interval at which an edge point is extracted, respectively(it means that edge-point extraction interval is set to equal toelectron beam scanning interval). All roughness index values obtainedunder these conditions will be discussed below. That is, whenintegration is discussed on a power spectrum, the integration range isassumed to be 1/L to 1/(2Δy).

Let σ_(e) contained in data averaged with an averaging parameter S beσ_(e) (S). Then the following relationship holds:σ_(e)(S)=σ_(e)(1)/√{square root over (S)}  Ex. 5

This expression itself represents a well-known statistic property and isused in the present method.

A stream of this method will be summarized below. Let σ_(m) (S) be thevalue of a line-edge roughness index obtained from the averaged data.First, a value of the line-edge roughness index, σ_(m) (1), iscalculated from data not subjected to the averaging processes. Then, theimage is averaged to obtain a line-edge roughness index. Line-edgeroughness index is preferably calculated for plurality of S values. LetS_(min) and S_(max) be a minimum value and a maximum one, respectively,of averaging parameters S to be used for the analysis. Then, we have aset of values (S₁, σ_(m) (S₁)), (S₂, σ_(m) (S₂)), . . . (S_(N), σ_(m)(S_(N))) where S₁=1. Although described later, S_(min) and S_(max) mustbe set carefully.

In the third method, these data are simply fitted in Ex. 1. In thiscase, using Ex. 5, the following expression is given:σ_(m)(S)=√{square root over (σ₀ ²+{σ_(e)(S)}²)}=√{square root over (σ₀²+{σ_(e)(I)}² /S)}  Ex. 6

In fitting, σ₀ and σ_(e) (1) are used as fitting parameters.

A value of σ₀ thus obtained is defined as a real roughness index value,which is the third solving method. This method corresponds to performingthe first method, avoiding Fourier's transform. The square of σ_(m) (S)obtained from data observed usually corresponds to an integrated valueof a spectrum including noise in FIG. 4. A value of σ₀ ² to be obtainedcorresponds to integration of the real spectrum in FIG. 4 whileintegration of a dotted area is {σ_(e) (S)²}. This corresponds to takingdata by changing S and fitting the S-dependence of integration of thedotted area with {σ_(e) (1)²/S}. There are two fitting parameters. Thus,for fitting purposes, at least two sets of values of measured data to befitted are needed. That is, N≧2.

(4) Fourth Method

It should be noted in the third method that as explained in FIG. 5 andthe description of the second method, when the value of S is large, highfrequency components of the line-edge roughness are cut and notcontained in the measured values. Assume now that when the value of theaveraging parameter is S, noise is sufficiently reduced. FIG. 7schematically illustrates a power spectrum in which noise issufficiently reduced by S-averaging operation. A graph of FIG. 7 isplotted based on vertical and horizontal axes marked off in logarithms.In the spectra of resist pattern roughness reported so far, a maximumvalue of a frequency f₀ at a boundary point in the spectrum shape is0.008 nm⁻¹. That is, the power spectrum density can be considered to bedirectly proportional to f⁻² in at least an area where f>0.008 nm⁻¹. Thegraph of FIG. 7 is drawn based on this fact and also shows arelationship in magnitude between that value, 1/(2SΔy) that is a minimumvalue of a frequency area where the power spectrum density is greatlyreduced when the data is averaged with the averaging parameter S, and1/(2SΔy) that is a limit of the frequency of the roughness discussedherein.

The first or third method corresponds to neglect of the presence of theFIG. 7 hatched area. Considering that the vertical axis of the graph ismarked off in logarithms, a proportion of the whole roughness index thatthe hatched area of FIG. 7 occupies is small and when S is small, thereis no problem with the first or third method. More specifically, whenthe length L of the examination area is 1 micron or more and the productof S and Δy is 50 nm or less, the first or third method will suffice forthe evaluation of the roughness. The reason for this is as follows: Inmany cases, many users desire to set L to a value of more than 1 micronto understand dispersion of the transistor performance. In this case,when the spectrum of the roughness of the resist observed so far isanalyzed and the product of S and Δy is 50 nm or less, the area of ahatched part of FIG. 7 to be observed by the averaging occupies 90% ormore of the whole hatched area. That is, the value of σ to be observedis 95% (or the square root of 90%) or more and it is considered thateven when the influence of the hatched part is neglected, sufficientlyaccurate measurement is achieved.

Under the conditions where a percentage of the whole roughness indexthat the area of the hatched part of FIG. 7 occupies is relativelylarge, a quantity corresponding to the hatched part of FIG. 7 need becorrected for the roughness index to be obtained (in the second method,the correction quantity is presumed by assuming that the high frequencyarea spectrum is represented by an approximate curve). In a solvingmethod to be described below, a correction term is added to Ex. 6 forcorrecting purposes. That is,

$\begin{matrix}\begin{matrix}{{\sigma_{m}(S)} = \sqrt{\sigma_{0}^{2} + \left\{ {\sigma_{e}(S)} \right\}^{2} - \left\{ {\sigma_{LOST}(S)} \right\}^{2}}} \\{= \sqrt{\sigma_{0}^{2} + {\left\{ {\sigma_{e}(1)} \right\}^{2}/S} - \left\{ {\sigma_{LOST}(S)} \right\}^{2}}}\end{matrix} & {{Ex}.\mspace{14mu} 7}\end{matrix}$where the square of σ_(LOST) (S) represents a dispersion calculated fromthe cut high frequency components and corresponds to the hatched part ofFIG. 7. In order to fit a result of the measurement using this Ex. 7,the S-dependence of σ_(LOST) (S) must be known beforehand. In thefollowing, two methods, i.e., fourth and fifth solving methods, usingEx. 7 will be described.

First, the fourth method will be described. While described withreference to Ex. 4, a spatial frequency distribution of line-edgeroughness that will be naturally generated has a property that the powerspectral density is inversely proportional to the square of frequency f²in the high frequency area.

A lower limit f₀ of the high frequency area referred herein (or an areawhere the power spectral density is inversely proportional to the squareof frequency f) depends on the resist material and a patterning processemployed. (Hereinafter, the unit of frequency should be represented bynm⁻).

The power spectral density PSD (f) in an area where f>f₀ is obtained byintegrating the hatched part of FIG. 7 and σ_(LOST) (S) satisfies:σ_(LOST)(S)²=2AΔy(S−1)  Ex. 8Substituting this expression into Ex. 7, we have:σ_(m)(S)=√{square root over (σ₀ ²+{σ_(e)(1)}² /S−2AΔy(S−1))}{square rootover (σ₀ ²+{σ_(e)(1)}² /S−2AΔy(S−1))}  Ex. 9

The data measured need be fitted, using this expression with σ₀, σ_(e)(1) and A as fitting parameters. In this case, three sets or more ofmeasured values are needed. That is, N≧3 is required. S and Δy mustsatisfy 2SΔy<1/f₀ nm where f₀ is a bending point on the spectrummentioned above. Although its physical origin is not clear, it isconfirmed in every resist pattern that f₀ is 0.008 nm⁻¹ or less. Thus,SΔy need be set so that 2SΔy<1/125(nm⁻¹).

(5) Fifth Method

In this paragraph, another fitting method using Ex. 7 (or a fifthsolving method) will be described. Since the number of fittingparameters is large in the fourth method, the value of A or itsalternative variable is calculated beforehand in this method. Thiscorresponds to advance calculation of information in the high frequencyarea. There are three kinds of methods of calculating the value of A ora corresponding quantity. In the following, each method will bedescribed below.

Method 5-1

First, a first method of calculating the value of A or its correspondingquantity will be described. As described with reference to the fourthmethod, the high frequency area of the power spectrum of the roughnessis represented by a simple function such as Ex. 4. Thus, it will beeasily known that the dotted part of FIG. 7 is also represented easilyby A (1/f₁−2SΔy). Then, the image is averaged using S₀ as the averagingparameter value, thereby reducing noise sufficiently. Then, anexamination area L is set to 1/f₀ nm or less, thereby acquiring imagedata, and then line-edge roughness index σ_(A) is calculated based onthe image data. Of course, in this case length L along a line of theexamination area must be shorter than the inverse of 0.008 nm⁻¹ or 125nm because otherwise, the integration range would contain an area otherthan that where the spectrum is represented by Ex. 4 and cannot beexpressed in a simple expression. Then,σ_(A) ² =A(1/f ₁−2S ₀ Δy)  Ex. 10is solved, thereby obtaining constant A, which is then substituted intoEx. 8. This fixes σ_(LOST) (S) in Ex. 7, which can be written as:

$\begin{matrix}{{\sigma_{m}(S)} = \sqrt{\sigma_{0}^{2} + {\left\{ {\sigma_{e}(1)} \right\}^{2}/S} - {2\;\Delta\;{y\left( {S - 1} \right)}{\sigma_{A}^{2}/\left( {{1/f_{1}} - {2S_{0}\Delta\; y}} \right)}}}} & {{Ex}.\mspace{14mu} 11}\end{matrix}$using this expression, measured data σ_(m) (S) should be fitted with σ₀and σ_(e) (1) as the fitting parameters.

As in the fourth method, expression f₀≦f₁<1/(2SΔy) and furtherf₀≦f₁<1/(2S₀Δy) must hold. In many cases, f₀<<1/(2S₀Δy). In such a case,2S₀Δy of the right side of Ex. 11 may be neglected.

In order to calculate the value of σ_(A) correctly in performing thismethod, a plurality of examination areas should be set along theline-edge of the pattern, image data on these examination areas shouldbe measured and then an averaged value of the squares of edge roughnessindexes, σ_(A), should be calculated. As the number of areas formeasurement is larger, a better result is obtained. According to a ruleof thumb, if the measurement is made until a total of lengths of themeasurement areas amounts to approximately 2 microns and resultingvalues are averaged, dispersion will be reduced sufficiently. In orderto calculate σ_(A) accurately, σ_(A) need not be measured actually eachtime in addition to the usual observation. This is because although anerror involving σ_(A) is σ_(LOST) (S), this σ_(LOST) (S) itself is notso large in usual observation, its influence on σ₀ and σ_(e) (S) is verysmall.

Method 5-2

A second method (hereinafter referred to as method 5-2) of calculatingthe value of A or a corresponding variable will be described next. Thismethod is substantially the same as method 5-1. In method 5-2, the valueof A is calculated using the fourth method. First, an image of highmagnification (or small Δy) where an image of an object appears isprepared and examination areas are set on an edge of the objectappearing on the image. In the set examination areas, data series{Δx_(i): Δx₁, Δx₂, . . . } and {Δw_(i): Δw₁, Δw₂, . . . } of the edgeroughness are calculated and then the obtained data serieses areprocessed statistically, thereby obtaining σ_(m) and 3σ_(m) as theroughness bias indexes. In addition, the averaging parameter S ischanged and the averaging process is performed on each data series witha respective one of different averaging parameters S to obtain acorresponding roughness bias index for a respective data series obtainedwith the respective one of the different parameters S. As describedabove, the S-dependability of the roughness bias index is calculated andA is calculated in the fitting process (where the number of fittingparameters is 3) using the fourth method using Ex. 9. By calculating Abeforehand like this, a data series of the edge roughness obtained usingany L can be analyzed in the fitting process (where since A is knownalready, the number of fitting parameters is only two; σ_(o) and σ_(e)(1)) using Ex. 9.

Any length L may be taken along the edge of the examination area when Ais calculated, but it is preferably selected as long as possible underthe conditions that the image is of a sufficiently high magnification.Roughness varies from place to place. Thus, when L is short, the valuesof A would vary. Thus, preferably, the values of A are calculated andaveraged in as many places as possible. It means that the fourth methodis performed many times, that is, it needs times and skill. However, asL increases, the reliability of values of A to be calculated willincrease and hence L should be increased preferably. According to thepresent method 5-2, the roughness index can be obtained with highaccuracy compared to the method 5-1, and unlike method 5-1, there is nolimit to the length L of the examination area.

Method 5-3

In order to obtain the value of A or a corresponding variable value inthe fifth method, another method can be considered (hereinafter referredto as method 5-3). Also in the method 5-3, the fourth method is used toobtain the value of A. First, in order to obtain the value of A, animage of a small Δy is prepared as in method 5-2. The S-dependence ofthe roughness value is calculated on a pattern edge of the preparedimage. In this case, unlike method 5-2, a small examination area lengthL is taken. According to a rule of thumb, a maximum value of L is 125 nmand preferably 100 nm or less. Under these conditions, the wholefrequency areas of roughness to be detected are in a high frequency areawhere the power spectral density conforms to Ex. 4. Thus, integration ofEx. 4 is the square of σ_(A). That is, we obtain:

$\begin{matrix}{\sigma_{A}^{2} = {{\int_{1/L}^{{1/2}\;\Delta\; y}{{A/f^{2}}\ {\mathbb{d}f}}} = {A\left( {L - {2\;\Delta\; y}} \right)}}} & {{Ex}.\mspace{14mu} 12}\end{matrix}$where L and Δy are an examination area length and a scanning lineinterval, respectively, in the measurement for obtaining the value of Abeforehand. By substituting the L and Δy into Ex. 7, one of A and σ_(A)can be erased. If, for example, A is erased, we obtain

$\begin{matrix}{{\sigma_{Am}(S)} = \sqrt{{\sigma_{A\; 0}^{2}\left\{ {1 - \frac{2\;\Delta\;{y\left( {S - 1} \right)}}{L - {2\;\Delta\; y}}} \right\}} + \frac{\left\{ {\sigma_{e}(1)} \right\}^{2}}{S}}} & {{Ex}.\mspace{14mu} 13}\end{matrix}$where the value of σ_(A) obtained after the averaging operations wereperformed with the averaging parameter S was expressed as σ_(Am) (S),σ_(A0) represents σ_(A) free from the influence of noise, and σ_(e) (1)the influence of noise on this image (for obtaining A or σ_(a)). In thiscase, σ_(A0) need be obtained by fitting according to Ex. 13 and thensubstituted as a real σ_(A) into Ex. 11. Note that since the value of Lis small when σ_(A) is calculated, σ_(A0) are preferably measured inseveral places and fitted, thereby obtaining an averaged value.

Once σ_(A) or A is calculated in any of the methods 5-1, 5-2 and 5-3, itcan be used for analysis of patterns of the same design size createdwith the same materials in the same process. Among these three methods,method 5-1 that uses no fitting to obtain A or σ_(A) requires a shortestcalculation time. Method 5-2 provides high accuracy and requires theoperator to do a smallest quantity of work. Thus, method 5-2 is suitablefor automation of the analysis work. Method 5-3 has a merit that as thenumber of measurement places increases, the measurement accuracyimproves greatly.

A maximum one of values of f₀ observed in various resist patterns so faris 0.008 nm⁻¹, which is preferably used as the value of f₀. For example,125 nm is used as the value of L.

In the above, the third method using Ex. 6 and the fourth and fifthmethods using Ex. 7 have been illustrated. In any of these methods, onlyone fitting operation is required and a Fourier's conversion process canbe omitted which imposes a burden on the calculation unit compared tothe first and second methods that performs the averaging operations withthe plurality of averaging parameter values, thereby obtaining edgeroughness. Use of the third-fifth methods allows an error σ_(e) ofroughness due to random noise to be quantified in a short time. Inaddition, a real roughness index value σ₀ can be calculated and hencehigh-accuracy roughness of high throughput can be measured.

In the above, the principle of the means for obtaining roughness indexeshas been described in each of the first-fifth methods. Since the firstor second method includes the step of observing a spectrum visually, ithas a merit that the user can immediately notice the occurrence ofroughness having a peculiar period due to the influence of a mask or aperipheral pattern. Thus, this method is suitable for analysis of thecharacteristics of line-edge roughness of a circuit pattern in thesemiconductor manufacturing process and/or a study of development ofdevices. The third method is suitable for analysis of an image in whicha long area along the edge is observed at very fine scanning intervalsbecause the ratio of σ_(LOST) (S) to the whole roughness is small. Whena length along a line of the observation area is short or the scanningline intervals are large, a relative value of σ_(LOST) (S) to roughnessto be measured is large. Thus, correction is required. Accordingly, insuch a case the fourth method in which accurate measurement is possibleby correction is suitable. In addition, when the number of scanninglines is small or the magnification of a (y-) direction along the edgeis low, the fourth method is suitable because in such a case, Δy islarge and a high frequency area on the spectrum is not observed, andhence the value of A cannot be obtained possibly in the fourth method inwhich the value of parameter A is fitted based only on the obtaineddata. If the fifth method in which σ_(A) S obtained beforehand from animage observed with higher magnification is used, A is determined withhigh accuracy and σ₀ and σ_(e) can be calculated accurately.

In the third, fourth and fifth methods, the results can vary dependingon whether which area involving the actually measured values (or rangeof values of S) should be used for fitting purposes. There are tworeasons: first, an edge detection error will occur which cannot bedescribed only with σ_(e) when S is too small, and second, when S is toolarge, the power spectrum cannot be described in Ex. 4. In order todetermine a minimum value S_(min) of S, the position of an edge pointdetected should be viewed during measurement and whether the position isappropriate or not should be confirmed. According to experience of theinventors, it is known that when a stay time per pixel of an observingbeam (or a total time for which the observing beam was applied to onepixel) is approximately 2 μs or less, S_(min) should be 3 or more. Themaximum value S_(max) should be selected such that a value of2×S_(max)×Δy is smaller than 1/f₀. It can also be said empirically thatS_(max) should be selected such that 2×S_(max)×Δy equals 125 nm or less.

When the fifth method is employed for the reason that Δy is large asdescribed above, the obtained roughness index value corresponds to avalue obtained by sampling the edge at intervals of Δy. However, evenwith this interval the sampling density can be insufficient. In thiscase, high frequency parts of the power spectrum that cannot be detectedat the sample intervals of Δy can be calculated using σ_(A) and added,thereby calculating a value corresponding to the roughness measured atvery small sample intervals.

By expressing the aforementioned algorithm with software, implementingthe software on information processing means such as a computer andusing the software for analysis of image data obtained from appropriateimage data acquiring means, the problem of the present invention will besolved. While data obtained from the scanning electron microscope isused often as the image data, the present invention is applicable toanalysis of all image data such as transmission electron microscopeimages and X-ray images.

The high-accuracy pattern shape evaluating method and apparatusaccording to the present invention has the function of quantifying theinfluence of random noise on line-edge roughness when a fine pattern isobserved with the scanning microscope and calculating a value closer toreal edge roughness by subtracting the quantified noise value from themeasured value. In addition, these calculations can be performed basedon a single sheet of observation image. In this calculation, the userneed not perform a complicated operation such as parameter setting.Thus, high-accuracy roughness measurement can be performed easily in ashort time even from an image of high noise, thereby allowing the finerpattern shape to be evaluated. This produces an advantageous effect thatthe examination time is reduced and deformation/damage of the pattern inobservation is restricted, advantageously. Thus, in fine working,development of materials and processes and screening can be performedaccurately with a low damage. Even in mass production process,high-accuracy examination is achieved, thereby improving productivity.

The influence of random noise quantified can be used as a noise index ofthe device. Using this result, it can be determined whether theobservation conditions are good or not (for example, whether themicroscope is in focus). By measuring and preserving this index over along time, a long-time stability of the device performance can beevaluated, thereby improving productivity.

Other objects, features and advantages of the invention will becomeapparent from the following description of the embodiments of theinvention taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates a relationship between the x-directiondependability of a secondary electron signal intensity or profile and across-section of an actual pattern.

FIG. 2 schematically illustrates a relationship between a schematic viewof a SEM image in the vicinity of a line pattern edge and edge roughnessΔx_(i).

FIG. 3 schematically illustrates a relationship between schematic viewof a SEM image of a line pattern edge and line width roughness Δw_(i).

FIG. 4 is a schematic diagram of a power spectrum of real edge roughnessthat illustrates the influence of random noise on the power spectrum.

FIG. 5 is a schematic diagram of a power spectrum of edge roughness thatillustrates the influence of image data averaging operation in ay-direction on the power spectrum.

FIG. 6 illustrates a relationship between approximate power spectrum ofedge roughness and roughness index calculated from the power spectrum.

FIG. 7 illustrates a relationship between a value of roughness indexobtained from the averaged data and a roughness component not includedin the index value due to the averaging.

FIG. 8 illustrates a rectangle indicative of observation image data andan examination area appearing on an examination device display picturein Embodiments 1, 2 and 3 of the present invention.

FIG. 9 illustrates a power spectrum of edge roughness obtained inEmbodiment 1.

FIG. 10 illustrates a power spectrum of edge roughness obtained inEmbodiment 2 and an approximate curve.

FIG. 11 is a flowchart indicative of a process of calculating andanalyzing a roughness index from image data that will be performed inEmbodiments 3, 4 and 5 of the invention.

FIG. 12 is a flowchart indicative of detailed procedures of step 1101 ofcalculating a roughness index from image data, which step will beperformed in Embodiments 3–5.

FIG. 13 is a flowchart indicative of the details of step 1102 inEmbodiment 3 analyzing a roughness index obtained from the image data.

FIG. 14 schematically illustrates a display of a result of analysisobtained in Embodiment 3.

FIG. 15 is a flowchart indicative of the details of step 1102 inEmbodiment 4 analyzing a roughness index obtained from the image data.

FIG. 16 schematically illustrates a display of a result of analysisobtained in Embodiment 4.

FIG. 17 is a flowchart indicative of the details of step 1102 inEmbodiment 5 analyzing a roughness index obtained from the image data.

FIG. 18 schematically illustrates the structure of an examination deviceused in Embodiment 4.

FIG. 19 schematically illustrates a chip layout of wafer examined inembodiment 4.

FIG. 20 schematically illustrates the structure of an in-line lengthmeasurement/roughness analysis system.

FIG. 21 illustrates an examination recipe picture for in-linemeasurement of Embodiment 5.

FIG. 22 illustrates a screen for designating a picture region forcalculating parameter A on an examination recipe.

DETAILED DESCRIPTION OF THE INVENTION

(Embodiment 1)

This embodiment illustrates application of the first method to a CD-SEM,which will be described next.

FIG. 18 schematically illustrates a hardware structure of the CD-SEMused in this embodiment. The CD-SEM mainly comprises housing 1801 of ascanning electron beam microscope that comprises an optoelectronic (orSEM) column and a specimen chamber, a control system 1811 for themicroscope and information processor 1812. Information processor 1812 isconnected to a data storage device 1813 that stores an obtained scannedelectronic image and CAD data necessary for analyzing purposes. Datastorage device 1813 can be provided within information processor 1812.Although not shown, information processor 1812 comprises an informationinput terminal that an operator of CD-SEM inputs information necessaryfor data processing to information processor 1812 and an image displaymeans that displays a scanned electronic image acquired. A specifiedinformation input terminal may include a keyboard, a mouth or an GUIpicture that will be displayed on the image display means.

The optoelectronic column comprises electron beam gun 1802, focusinglens 1804, deflector 1805, objective lens 1806, and detector 1810. Thespecimen chamber comprises a stage 1808 on which examination wafer 1807is placed as an object to be examined. Secondary electrons 1809 producedfrom wafer 1807 by irradiation of electron beam 1803 from electron beamgun 1802 are detected by detector 1810, and converted by control system1811 to digital data, which is then transferred to information processor1812, thereby producing image data to be used for analyzing purposes.

In this embodiment, image data of the object was acquired in patternobservation using the scanning electron microscope provided on theCD-SEM. The acquired image data is then preserved in data storage device1813. After the observation, the information input terminal is operatedto analyze image data, thereby obtaining a roughness index.

First, an image of a pattern from which the roughness index is to beacquired was displayed on the monitor picture. FIG. 8 schematicallyillustrates a SEM image of the pattern analyzed in this embodiment. Theimage of FIG. 8 was obtained by averaging secondary-electron signalintensities obtained in 32 scanning operations performed on an ArFresist line pattern from an upper left corner to a lower right corner ofthe visual field. The number of pixels of the observation image is 1500in vertical and horizontal directions with one side of each pixelcorresponding to 1 nm. That is, the length of the observation image inthe visual field was 1.5 μm in each of vertical and horizontaldirections. For emphasizing purposes, in FIG. 8 a flat area in which thesecondary electron intensity is low is illustrated as a dotted area andan area indicative of the vicinity of an edge of the line pattern isillustrated by a white part. Examination areas 803 and 804 are set inthe vicinity of the center of the FIG. 8 image. Examination areas 803and 804 are set by the operator of the CD-SEM and in this embodimenteach of the examination areas comprises a rectangular area of 1024 by 50pixels. This area was placed on an edge (or area 802 indicative of thevicinity of the edge) to be analyzed by manipulating the mouth. At thistime the examination areas are denoted by 803 and 804.

When examination areas 803 and 804 are set, a request to input setvalues necessary for extracting a data series of edge roughness isdisplayed on the GUI picture. The device user sets information necessaryfor extracting the data series, which includes a sampling interval fordata extraction in the y-direction, a noise reducing parameter in thex-direction, an averaging parameter S in the y-direction, etc. Insteadof the sampling interval for data extraction in the y-direction, thenumber of detection points may be set. When input of the requiredinformation is terminated, confirming icons such as “Detection areasetting has ended”, “Data series extraction setting has ended”, etc. aredisplayed on the GUI picture. When the device user clicks any one of theicons, a task that extracts a data series of the edge roughness in thearea starts to be executed.

When this task starts, the CD-SEM information processor calculates aprofile corresponding to a y-coordinate of a sampling position frompixel data in each of examination areas 803 and 804 in accordance withthe set data extraction start point and set sampling interval and thencalculates x-coordinate data indicative of the edge point from theprofile. This process is shifted and performed one after another inaccordance with the sampling interval in the y-direction and finallydata series {Δx_(i): Δx₁, Δx₂, . . . } or {Δw_(i): Δw₁, Δw₂, . . . } ofthe edge roughness are obtained in each examination areas 803 and 804.

In order to confirm the influence of the averaging operation visually,in this embodiment S was set to 1 first. As a y-coordinate at which thedata extraction started, a y-coordinate corresponding to a lower side ofeach of the examination areas 803 and 804 was set, and the samplinginterval was set to 1 nm. Edge points in the examination area wereextracted at intervals of 1 nm from image data where S=1, or unaveragedimage data, thereby extracting 1024 point positions (x₁, y₁), . . . ,(x_(i), y_(i)), . . . (x₁₀₂₄, y₁₀₂₄). An averaged line width of thepattern calculated from the data series obtained was 110 nm.

Then, by approximating an arrangement of the obtained points with thefollowing straight line, the values of α and β as the fitting parameterswere calculated:x=αy+β  Ex. 14

An i^(th) deviation Δx_(i) of an i^(th) edge point from the straightline was calculated in accordance with:Δx _(i) =x _(i)−(αy _(i)+β)  Ex. 15

In this way, edge roughness series {Δx_(i)} was produced, which isdefined as a series of edge roughness obtained at an averaging parameterS=1.

When the task of extracting the data series of edge roughness isterminated, a power spectrum obtained by Fourier's transform of the edgeroughness series of 1024 data items is displayed on the GUI picture.When the power spectrum is displayed, a request to ask the user whetheror not the averaging parameter S need be reset is displayed on the GUIpicture. When the user inputs an answer that the resetting of S isneeded to the information processor, the request to reset S is displayedon the GUI picture. The device user inputs a new S value in accordancewith instructions of the GUI. In this case, the information processormay have software that resets a noise reducing parameter in thex-direction in addition to the averaging parameter S. When an answerthat resetting of S is not required is inputted to the informationprocessor, the analysis ends at this point of time.

In the present embodiment, the horizontal noise reducing parameterremains fixed to 3 and each time S is incremented by one, they-direction averaging operation is performed on the original image,thereby obtaining an edge roughness series from the image, and powerspectrums obtained one after another by Fourier's transform aredisplayed on the same graph.

FIG. 9 shows a state of the display picture obtained by repeating theresetting of averaging parameter S until S=3. Appearance of an image inwhich the power spectrum density of the high frequency area at S=3 isdirectly proportional to 1/f² was confirmed visually. Since even when Swas 4 or more, noise (due to roughness in the high frequency area)remained materially unchanged, it was determined that S=3 wasappropriate.

Edge points were extracted using image data on which the averagingoperation was repeated until S=3 based on that result, a power spectrumwas obtained from 1024 data items and their σ was calculated as 1.20 nm.In order to obtain a profile at the sampling position of y=i after theaveraging operation when S>2, profiles at y values of from i+1−S/2 toi+S/2 when S is an even number are averaged, and profiles at y values offrom i−(S−1)/2 to i+(S−1)/2 when S is an odd number are averaged. Thus,information on image data present outside the set examination areasactually will mix. When a difference between the number of pixels of theoriginal image in the y-direction and the number of pixels of ay-direction length of the set area is smaller than S, an error isdisplayed. A line-edge roughness index in 1 μm of the examination arealength was recorded as 1.20 nm. The definition may be changed so as toemploy 3σ instead of σ.

It is known that when roughness indexes are obtained by fixing theaveraging parameter to 3 and then the respective roughness indexes areobtained for subsequent line pattern images of the same observationconditions, the influence of noise will decrease. Thus, the examinationwas performed so.

In the past, S=2 was employed uniformly in all the examinations withoutoptimizing the value of S. Thus, although values containing much noisewere obtained when the number of additions of secondary electronintensities was small, these values were used for pattern examination.Thus, even a pattern in which the roughness is not so large was regardedas having a bad (or very rough) shape and the lithography step wasperformed over again. In contrast, by using the present method thatincludes changing S, displaying the spectrum and then confirming asituation in which noise is reduced, high-accuracy roughness measurementis achieved and productivity of the semiconductor manufacturing processor apparatus improves.

While in the present embodiment the edge roughness was described, aroughness in the line width may be similarly analyzed. In this case, anexamination area need be set also on another edge of the same line whenthe examination areas are set. This additional examination area isdenoted by 804 in FIG. 8. Then, 1024×2 point positions on the left andright edges are obtained and denoted by (x_(L1), y_(L1)), . . . (x_(Li),y_(Li)), (x_(L1024), y_(L1024)) and (x_(R1), y_(R1)), . . . (x_(Ri),y_(Ri)), . . . (x_(R1024), y_(R1024)), respectively. Now, a local linewidth w_(i) is defined as follows:W _(i) =x _(Ri) −x _(Li)  Ex. 16

If this set {w_(i)} is replaced with {Δx_(i)}, subjected to Fourier'transform and then analyzed, line width roughness will be discussedinstead.

(Embodiment 2)

The present embodiment relates to application of the second method tothe CD-SEM, which will be described next. In order to describe thepresent embodiment, FIGS. 8, 9 and 10 will be used. The CD-SEM used inthis embodiment has exactly the same hardware structure as the firstembodiment. Thus, in the following, the description of Embodiment 1concerning FIG. 18 will be used as requested.

FIG. 8 schematically illustrates a SEM image of a pattern analyzed inthe embodiment. FIG. 9 illustrates a display picture obtained byrepeating the resetting of averaging parameter S until S=3. A processranging from the setting of examination areas 803 and 804 of FIG. 8 toacquisition of the power spectrum of FIG. 9 is exactly the same as thatof Embodiment 1.

As described in Embodiment 1, advent of the circumstances in which thepower spectrum density of the high frequency area was directlyproportional to 1/f² when S=3 was confirmed visually. On the other hand,however, the power spectrum density of an area where f>0.15 is extremelyreduced in the graph at S=3 because since S is large, short-periodcomponents are erased. In order to cope with situation, this area isapproximated with a function directly proportional to 1/f².

When in the present embodiment the CD-SEM operator inputs an answer thatthe resetting of S is not needed to the information processor, a messagerequesting to ask whether or not data missing in the high-frequency areadue to the averaging operations should be compensated for is displayedon the GUI picture. When the operator inputs that compensation for thehigh frequency area data is needed to the information processor, the GUIpicture displays a message requesting to input designation of a dataarea to produce an approximate curve in the high frequency area. Theoperator then sets data to set the approximate function, or upper andlower limits of the frequency area for the power spectrum, in answer tothe message. The operator sets the upper and lower limits for anappropriate range in the x-axis direction for the power spectrum at S=3shown in FIG. 9 by moving a pointer such as a cursor. In the presentembodiment, the approximate curve calculation area was set for0.03<f<0.15.

When inputting the approximate function calculation area is terminated,information processor 1812 provided in the CD-SEM calculates a functionapproximating to the function of Ex. 4 by using data on the powerspectrum in the set frequency area, calculating the value of A as thefitting parameter, and hence providing an approximate function. FIG. 10schematically illustrates a picture on which the approximate functionobtained is displayed superimposed on the power spectrum and the highfrequency area from which data is missing due to the averagingoperations is extrapolated. The approximate function obtained isrepresented by broken line 1001 in FIG. 10. This function is extendedinto an area where f>0.15 with the extended part shown by thick soldline 1002. In the area where data is missing or f>0.15, extrapolatedvalues obtained from the approximate function are used for the spectrumdata. That is, in f≦0.15 nm⁻¹ and f>0.15 nm⁻¹ areas, the spectrumobtained from the measured values, and solid line 1002 were used as thespectra parts obtained when noise was reduced sufficiently.

Then, this spectrum was integrated, thereby obtaining a valuecorresponding to the square of roughness index σ. As a result, σ was1.22 nm.

This invention produces the same merits as described in Embodiment 1,and furthermore, σ can be measured more accurately than in the firstembodiment.

(Embodiment 3)

The present embodiment relates to application of the third methoddescribed in “Summary of the Invention” to the CD-SEM, which will bedescribed next. The image data analysis method which will be describedin the present embodiment comprises obtaining an index of roughness andan index of random noise occurring in the image without performingFourier' transform from data used to calculate the roughness inEmbodiment 1. In the description of the present embodiment, FIGS. 8,11–14 will be used. FIG. 8 schematically illustrates a SEM image of apattern analyzed in the present embodiment. FIG. 11 is a flowchart of acalculation process performed in the present embodiment. FIGS. 12 and 13are flowcharts each representing a part of the process of FIG. 11. FIG.14 shows roughness indexes obtained from the image and a graph of afitting curve as a result of the analysis. The CD-SEM used in thepresent embodiment is exactly the same structure as used inEmbodiment 1. Thus, in the following description, the description ofEmbodiment 1 concerning FIG. 18 will be used as required.

Also in the present embodiment, a pattern is observed and its image datais preserved as in Embodiment 1 and 2. After the observation, thecomputer terminal is operated to analyze the image data, therebyobtaining roughness indexes.

First, an image of a pattern from which the roughness indexes are to beobtained is called from data storage device 1813 and displayed on themonitor picture. The present embodiment uses the same observation imageas Embodiments 1 and 2. The number of pixels in the visual field is 1500in each of the vertical and horizontal directions with one side of apixel corresponding to 1 nm.

Next, examination areas were set. Examination areas each 1024 pixelslong and 50 across were displayed at substantially the center of theimage and then placed on an area that contains an edge (or an area 802close to the edge) to be analyzed by mouth operation. In this way,examination areas 803 and 804 were set. FIG. 8 schematically illustratesa pattern image on which examination areas 803 and 804 are set on anexamination image called from data storage area 1813. While in thefollowing, analysis of examination area 803 will be described, analysisin examination area 804 will also be performed using the same method.

Then, referring to FIG. 11 the whole flow of an analysis algorithm to beused in the present embodiment will be described. The image dataanalysis to be performed in the CD-SEM of this embodiment is mainlycomposed of step 1101 of setting parameters and a range of datanecessary for acquiring a roughness index to be obtained from anexamination image, step 1102 of obtaining data on the averagingparameter S-dependency of an roughness index σ_(m) to be obtained fromthe examination image, and step 1103 of fitting the data and calculatinga contribution σ₀ of roughness present in the pattern and a roughnessindex bias value σ_(e) due to the influence of random noise.

When the examination areas are set on the examination image displayed onthe monitor picture, the analysis flow passes to step 1201, therebydisplaying a window on which parameters necessary for the analysis willbe set on a monitor picture. The parameters set in this step are dividedinto parameters to define an edge from a two-dimensional gray image andaveraging parameters in the respective x- and y-directions. The formerincludes a start point (or y-coordinate) where the edge roughness isextracted, and a sampling interval in the y-direction at which edge datais extracted. The latter includes a noise reducing parameter w in thex-direction, a minimum value S_(min) and a maximum value S_(max) ofaveraging parameter S in the y-direction. In the present embodiment, ay-coordinate of a lower side of the examination area 803 was set as thestart point of edge roughness extraction. Furthermore, 1 nm was set asthe sampling interval in the y-direction, 3 was set to S_(min), 9 toS_(max) and 3 to w, respectively.

When the parameters are set, the flow passes to step 1102. FIG. 12illustrates a more detailed flow of step 1102. Then, the details of aflow of producing data on the averaging parameter-dependency of theroughness index will be described, using FIG. 12.

When the respective parameters are set in step 1101 and the processoruser then clicks an ENTER button displayed on the GUI picture,information processor 1811 of FIG. 18 smoothes an x-direction signalusing the value of w set for pixels in examination area 803.

When the x-direction signals are smoothed, the flow passes to step 1202in which the value of averaging parameter S is initialized or set to 3.

The flow then passes to step 1203 in which information processor 1811performs a pixel operation on image data in examination area 803,performs a y-direction averaging operation on the examination area atthe set parameter value. Then the flow passes to step 1204 to extractedge points in the examination area where the averaging process wasperformed. In the present embodiment, edge points are extracted in unitsof a pixel at intervals of 1 nm in the vertical or y-direction accordingto the set values. The flow then passes to step 1205 where the values ofcoordinates of 1024 points (x₁, y₁), . . . (x₁₀₂₄, y₁₀₂₄) obtained inthe previous step were approximated with Ex. 13 using the method ofEmbodiment 1, thereby producing an edge roughness series {Δx_(i): Δx₁,Δx₂, . . . } according to the definition of Ex. 14.

Then, the flow passes to step 1206 where a standard deviation σ_(m) (S)on 1024 data items contained in the edge roughness series (S) wascalculated, and σ_(m) (S) and the value of S were stored in pair in datastorage device 1813. That is, data sets ((S_(min), σ_(m) (S_(min))),((S_(min)+1, σ_(m) (S_(min)+1)), . . . , ((S_(max), σ_(m) (S_(max)))were stored in data storage device 1813.

Then, the flow passes to step 1207 where information processor 1811determines whether the averaging process has-been completed based on thevalue of S. If S is smaller than S_(max), the flow passes to step 1208where the value of S is incremented by one and again the flow passes tostep 1203. A looping operation of steps 1203–1206 is repeated until Sequals S_(max) in step 1207, at which time the looping operation isterminated.

In the above steps, values σ_(m) (S) of from S=S_(min) (in thisembodiment, 3) to S_(max), (in the present embodiment, 9) are obtainedfrom the examination image, thereby terminating the flow of producingdata on the averaging parameter-dependency of the roughness index shownin step 1102 of FIG. 11.

Next, the data processing flow passes to step 1103 which is described indetail in FIG. 13, and the following description is given, using FIG.13.

When production of data on the averaging parameter dependency of theroughness index is terminated, the flow passes to step 1301 where setsof results (S_(min), σ_(m) (S_(min))), (S_(min)+1 σ_(m) (S_(min)+1)), .. . , (S_(max), σ_(m) (S_(max))) obtained are displayed as a graph onthe display picture. Then, the flow passes to step 1302 where thesepoints are fitted on assumption that these points follow Ex. 6 and thenthe values of σ₀ and σ_(e) (1) as the parameters are calculated. Note inthe present embodiment that σ_(e) (1) was used as σ_(e). Simultaneously,a fitting curve (obtained by substituting the parameter values obtainedby the fitting into Ex. 6) is plotted on the graph. FIG. 14 shows thisgraph. In the present embodiment, σ₀=1.49 nm and σ_(e) (1)=0.62 nm. Theresults were displayed on the graph and the fitting process wasterminated.

Thus, the process of FIG. 11 was terminated and σ₀ and σ_(e) wereobtained. The value σ₀ thus obtained was used as an index representing amerit of the shape of the observed pattern and σ_(e) was recorded as anindex representing a degree of noise occurring in the examinationdevice. Since these two parameters are obtained accurately and rapidly,the efficiency of pattern shape management and hence productivityimprove. The performance of the examination device is capable of beingmonitored over a long time, thereby improving productivity.

While in the present embodiment the edge roughness was calculated, linewidth roughness can be used as an index instead of the line-edgeroughness. In that case, as described at the end of Embodiment 1, rightand left edge points of the line pattern are extracted, the distancebetween the right and left edge points having the same y-coordinate iscalculated at each of y=1 through 1024 and then analysis similar to thatused for the edge roughness is required on the respective distancescalculated.

In the present embodiment, no free spectrum is involved, and hence thecalculation is simple and does not take much time. Since the function ofthe conventional length measuring SEM is used, any new calculationprogram need not be implemented into the examination device and thememory of the examination device is not pressured either. Since there isno process for determining an optimal S value using a visualobservation, there is a merit that analysis can be easily automatedcompared to the techniques of Embodiments 1 and 2.

As described above, by implementing software that embodies thealgorithms shown in FIGS. 11–13 on the information processor for theCD-SEM, thereby performing image data analysis, the CD-SEM producesexcellent advantageous effects described above.

(Embodiment 4)

The present embodiment relates to application of the fourth methoddescribed in “Summary of the Invention” to the CD-SEM, thereby acquiringan image in line while analyzing the roughness, which will be describednext. An object to be inspected is a semiconductor wafer having a resistlayer formed after being subjected to lithography. Length measurementand roughness analysis were performed.

FIG. 20 illustrates the structure of an in-line roughness analysissystem using the CD-SEM. Reference numeral 2001 denotes a SEM housingthat houses a photoelectric device for acquiring a SEM image such as anoptical system for electron beam irradiation, a secondary electrondetector and or a specimen stage. The inside of the SEM housing isevacuated so as to maintain a high evacuated state. Reference numeral2002 denotes a load lock chamber that acts as a spare vacuum chamber inwhich an examination wafer conveyed by a wafer conveyance system 2004 istemporarily stored before being conveyed into the SEM housing. Also,when the wafer is carried out of the SEM housing after the lengthmeasurement and image acquisition are terminated, the wafer is returnedto the conveyance system through load lock chamber 2002. FIG. 20illustrates a CD-SEM system with two separate load lock chambers intoand out of which the wafer is conveyed. Although not shown, waferconveyance system 2004 is connected to a wafer stocker such that historyinformation on a wafer conveyed into SEM housing 2001 (for example, lotinformation) is transferred every moment to information processor 2006.

Reference numeral 2005 denotes a SEM control system that controls therespective components of the SEM including, for example, various lensesthat compose the op to electric system and a drive voltage for theelectron gun and/or a quantity of movement of the specimen stage.Information processor 2006 analyzes acquired image data. Thus,information processor 2006 includes a memory on which various analysissoftware are loaded, an arithmetic device that executes the softwareand/or a large-capacity storage that stores the acquired data. Thelarge-capacity storage may be provided outside of information processor2006. For example, a dedicated server for storage of image informationmay be provided so as to be connected to information processor 2006.Reference numeral 2007 denotes a monitor that displays an SEM image of awafer acquired in SEM housing 2001 and a result of analysis performed byinformation processor 2006. Various numeral values necessary forexecution of the analysis by information processor 2006 are set byinformation input means 2008 connected to information processor 2006.SEM housing 2001, SEM control system 2005 and information processor 2006are connected through signal transmission cables 2009. For example, animage signal indicative of an examination specimen acquired by thesecondary electron detector provided within SEM housing 2001 istransmitted via SEM control system 2005 to information processor 2006.

Then, an image data acquiring process will be described. A wafersubjected to a lithography step is carried into SEM housing 2001 throughload lock chamber 2002. Information on the examination wafer carriedinto SEM housing 2001 is stored as an examination recipe already withininformation processor 2006. When the processor user starts up thesystem, or each time the history information on the examination wafercarried into SEM housing 2001 changes, the recipe is called throughmonitor 2007 and information input means 2008, and then variousparameters necessary for roughness analysis are set. When theseparameters have been set, wafer 2003 is placed on the stage within SEMhousing 2001, and then image data is acquired.

FIG. 19 illustrates layout of chips, whose roughness analysis will beperformed, on the examination wafer. For all or 44 chips on the wafer,line patterns of ArF resists 5·m long×100 nm wide present at the samerelative coordinates on the respective chips are to be inspected.Examination starts with chip 1902, proceeds to the right and thenreaches the right end of the uppermost chip. Then, examination shifts tothe right end chip of a row immediately below the uppermost row and thenshifts to the left. Finally, examination reaches to chip 1904, therebyterminating the examination on the single wafer. When image data of eachchip for analysis is acquired, the position of the specimen stage andthe position of electron beam irradiation are controlled such thatsubstantially the central position of the examination pattern withineach chip is the center of the visual field. Areas of the respectivechips having substantially the same coordinates and area and size arescanned by the electron beam, and secondary electron signals aredetected. These detected signals are transmitted along with informationon a specimen stage drive signal and an electron beam scanning signal toinformation processor 2006, converted to image data and then displayedas an examine pattern image on the monitor picture. An index (such as anidentifier) to discriminate each chip from other is added to arespective of all the chips on the wafer. Acquired image data of eachchip is stored along with its index in corresponding relationship intothe storage of information processor 2006.

A process of analysis of the acquired image data will be described next.FIG. 11 is a flowchart indicative of the process of data analysis to beexecuted by the CD-SEM in the present embodiment. Note that in thepresent embodiment all parameters to be set in step 1101 are alreadyregistered in an examination recipe stored in the storage. Thus,information processor 2006 reads out parameters and analyzes the data asrequired. When the flow passes to the data analysis step after imagedata acquiring step, an image of the examination area acquired isdisplayed on the monitor picture. In the case of the present embodiment,the displayed pattern image comprises 2500 pixels long by 2500 acrosswith one side of a pixel corresponding to 1 nm. This image was obtainedby averaging secondary electron signal intensities that were obtained in16 scanning operations each performed from an upper left corner to alower right corner of the visual field. The reason why the 16 scanningoperations were employed is to reduce damage to the pattern. However,this increased noise on the observation image.

First, an examination area is set automatically. Substantially the sameprocess as described with reference to embodiments 1–3 is performed byinformation processor 2006. In the present embodiment, the examinationarea corresponds to 2000 pixels long and 60 pixels across.

When the examination area is set, the analysis step shown in FIG. 11 isperformed automatically by information processor 2006. Also in thiscase, parameters to be set in the analysis are read out from theexamination recipe and set automatically. In the present embodiment, they-coordinate of a lower side of the examination area was set as a startpoint of edge roughness extraction; 1 nm as a sampling interval in they-direction; 3 as S_(min); 20 as S_(max); and 3 as w. Next, σ_(m) (S)data producing step 1102 of FIG. 11 is automatically executed. FIG. 12illustrates the detailed flow of step 1102 whose description will beomitted because it was described in detail in Embodiment 3. A differencebetween Embodiment 3 and the present embodiment is only that the flow ofFIG. 12 is executed automatically by the processor. Since the number ofpixels in the y-direction in the examination area is 2000, the number ofseries data items indicative of the edge roughness obtained finally is2000. In the above process, values σ_(m) (S) involving from S=3 to S=20were obtained.

Then, the flow passes to step 1103 that calculates σ₀ and roughnessindex bias value σ_(e). FIG. 15 illustrates a flow of step 1103 indetail. Description will be made below, using FIG. 15.

First, in step 1501, sets of results {(S_(i), σ_(m) (S_(i))}: {(S_(min),σ_(m) (S_(min))}, {(S_(min)+1, σ_(m) (S_(min)+1)}, . . . , {(S_(max)+1,σ_(m) (S_(max)+1)} obtained are displayed as a graph on the monitor.

Then, the flow passes to step 1502 where fitting is performed onassumption that these points on the graph conform to Ex. 9. Fittingparameters are σ₀, σ_(e) (1) and A. The least squares method was used asa fitting algorithm, thereby calculating values of parameters describingσ_(m) (S) obtained from the acquired image. In this case, σ_(e) (1) wasused as σ_(e). When σ₀, σ_(e) and a fitting curve (obtained bysubstituting the values of parameters obtained as a result of thefitting into Ex. 9) are calculated, the obtained numerical values andfitting curve are displayed superimposed on a graph of {(S_(i), σ_(m)(S_(i)) where i=min−max}. FIG. 16 shows this graph. In the presentembodiment, with a chip having an i^(th) index, results σ₀=21.70 nm andσ_(e)=0.80 nm were obtained. Thus, the process of FIG. 11 is terminated,and σ₀ and σ_(e) for a chip having that index were calculated.

The process for obtaining σ₀ and σ_(e) described just above wasperformed on a respective one of all the chips on the wafer of FIGS. 19and 44 measured values were obtained for each chip. A list of values σ₀and σ_(e) on the respective chips was stored as examination records ininformation processor 2006. A calculated averaged value of the values σ₀of all the chips (in the present embodiment, 44) was stored as typicalroughness values of wafer in information processor 2006, and an averagedvalue of the roughness index σ_(e) of all the chips was also stored asan index indicative of the state of the information processor 2006 onthe examination date in information processor 2006.

The calculation of the edge roughness indexes is as shown above, andacceptance or rejection of the process performed on the wafer can bemade using the calculated σ₀ and σ_(e). In the following, determinationof acceptance or rejection of a wafer using the whole chip average valueof σ will be described. In the present embodiment a criterion of σ₀ foraccepting a wafer before the examination has been determined. Thecontent of the criterion was that the average value of σ₀ was 2.50 nm orless and four of 44 examined chips should have σ₀ equal to, or largerthan, 3.00 nm. This content was obtained as the requirements formaintaining 70% or more of yield by performing simulation of transistorperformance and productivity. The criterion for acceptance has beenstored as an examination recipe in the storage of information processor2006. When the processor user sets an analysis sequence so as todetermine acceptance or rejection of wafers, the examination recipe isread out and acceptance or rejection is determined. An average value ofroughness indexes σ₀ of wafers examined in the present embodiment was2.50 nm and determined as acceptable.

In the prior art, very much noise is contained in an image acquired witha small averaged number of 16 operations in the present embodiment andthe averaged value of roughness indexes σ₀ obtained greatly tends to becalculated as a larger one than the real one. For example, in theprocessing of a wafer used in the present embodiment, the averaged valueof roughness indexes σ₀ calculated in the past was 3–4 nm and manyunacceptable wafers were produced. The unacceptable wafers are sent to areproducing process in which the resist is separated from the wafer,cleaned and then a resulting wafer is again subjected to the lithographyprocess. By using the present invention, a roughness close to the realvalue is measurable and it has been fined that the wafers determined tobe unacceptable so far are acceptable actually. Thus, productivity inthe manufacturing process improves.

Since the line-edge roughness analysis method of this embodiment needsno Fourier's transform, calculation is simple and can be made at highspeeds. Thus, the present invention is especially suitable for ananalysis system that requires a high throughput such as a roughnessanalysis in line. Since the present embodiment uses the function of aconventional length measuring SEM, no new calculation program need beimplemented on the examination device and no memory of the examinationdevice is pressured either. In addition, since contribution of highfrequency components to the roughness that cannot be detected due tonoise reduction has been corrected and hence the accuracy is high.

The method of this embodiment is suitable for analysis of an imageacquired at high magnification because when data points obtained in theactual measurement are fitted in the present method, results of enhancedreliability are obtained as the number of data points used for fittingpurposes increases. Increasing the number of data corresponds toincreasing S_(max). However, as described in the paragraph next to Ex.4, a usable value of S has a limit because if S is large, a maximumperiod of the roughness components to be lost due to the averagingoperations becomes larger than 1/f₀ (that is, the left end of thehatched part of FIG. 7 shifts further to the left from the left end ofthe dotted part) and Ex. 8 does not hold. Thus, when the scanning lineinterval Δy is, for example, 10 nm, S_(max) is 6 and only six measureddata items can be used to obtain three fitting parameters. If Δy is 2nm, 30 or more data items may be used for fitting purposes. Thus, thepresent method is suitable for analysis of a small Δy image or ahigh-magnification image.

While in the above description the observation and measurement of animage are illustrated as performed simultaneously, all images to beanalyzed may be acquired and then roughness may be measuredcollectively. In this case, the images are temporarily stored in thestorage of information processor 2006. In measurement, various parameterare set using monitor 2007 and information input means 2008 and then thesame analysis as mentioned in the previous examples is performed.

As described above, since the roughness indexes are obtained accuratelyand rapidly, the efficiency of pattern shape management and productivityimproved. By monitoring the value of σ_(e) as an index of theexamination device performance over a long time, productivity wasimproved.

While in the present embodiment the edge roughness was calculated, theline width roughness may be employed as an index instead of theline-edge roughness. In this case, as described at the end of Embodiment1 the right and left edge points of the life pattern are extracted,distances each between right and left edge points having the samey-coordinate need be sequentially calculated from y=1 to y=2000 as aline width roughness series, and then analyzed likewise as in the edgeroughness. While in the present embodiment the composition of thein-line measurement has been illustrated, this method is applicable tothe off-line measurement, of course.

(Embodiment 5)

The present embodiment relates to application of the 5-2 methoddescribed in “Summary of the Invention” to the CD-SEM, thereby acquiringan image in line while performing roughness analysis, which will bedescribed next. An object to be examined is a semiconductor wafer onwhich a resist layer was formed after being subjected to the lithographyprocess. The length measurement and roughness analysis were performed.For analyzing purposes, the system structure of FIG. 20 was used whichwas the same composition as that of Embodiment 4. Since the details ofthe system composition of Embodiment 4 have been already described, andfurther description of the system of FIG. 20 will be omitted. Theanalysis flow of the present embodiment passes basically along FIG. 11.The present embodiment is different from the other embodiments in thatthe former has an algorithm that calculates σ₀ and σ_(e), and beforehandcalculates fitting parameter A appearing in the algorithm. Next, aprocess to be performed before the flowchart of FIG. 11 will bedescribed.

When the system starts up or each time history information on anexamination wafer that is carried into SEM housing 2001 changes, theprocessor user calls the recipe through monitor 2007 and informationinput means 2008, and then sets an area for acquiring a parameter Acalculating image, an area in which length measurement and roughnessanalysis are performed, and various parameters necessary for theroughness analysis. The examination recipe cooperate with CAD data onthe examination wafer, thereby setting an image area on the CAD data.Thus, in the present embodiment, information processor 2006 is connectedto an external server that has stored the CAD data (not shown).

FIG. 21 illustrates one example of a display picture for the examinationrecipe of this embodiment. CAD display 2101 that displays a CAD image ofan area where the roughness analysis is performed actually composes theleft half of the display picture. In the CAD image of FIG. 21, an areapainted black appearing below a dotted rectangle corresponds to anactual wiring pattern. CAD display 2101 displays an identifier box 2103that indicates a management number of an examination wafer, a coordinateinformation box 2101 indicative of a part of the wafer corresponding tothe present displayed CAD image, and a visual-field size display box2105 that indicates how large the visual field of the present displayedCAD image is in each of the x- and y-directions.

Setting unit 2102 for a roughness analysis parameter is displayed on theright part of the display picture. Parameter setting unit 2102 has a setparameter display box 2106 indicative of various set parameters forroughness analysis. The processor user selects preferred numericalvalues from pull down menu 2107 corresponding to the respective setitems and inputs them. The roughness analysis parameters to be set onthe setting picture of FIG. 21 include, for example, x-directionaveraging parameter w, and minimum and maximum values S_(min) andS_(max) of y-direction averaging parameter S.

Now, when No. 5-2 is selected as an identifier of the algorithm that isused for roughness analysis, the set picture of FIG. 21 is switched tothat of FIG. 22. The No. 5-2 algorithm corresponds to method 5-2. Thisis because with NO. 5-2, parameter A need be determined before the stepsof calculating σ₀ and σ_(e) are performed. The set picture of FIG. 22 isfor setting areas from which spare images for calculating A areacquired. As shown in FIG. 22, elements 2201–2205 composing a part ofthe window are the same items as 2101–2105. The set picture of FIG. 22is different from that of FIG. 21 in the number of set areas fordetermining A, length Ln of each set area where n varies depending onthe number of set areas, and data sampling interval in each set area.The areas for acquiring the spare images are indicated by coordinatesdefault set in the processor or set arbitrarily by the informationprocessor or its user. In the present embodiment, the spare imageacquiring areas were set for calculation of parameter A in the vicinityof an area approximately 5 μm above an area for calculating σ₀ and σ_(e)to be set on the FIG. 21 set picture. When the spare-image acquiringarea are set, a CAD image displayed when the picture switches from FIG.21 to FIG. 22 is scrolled upward appropriately and the displaymagnification is further increased, thereby switching the CAD imagedisplayed on the picture. While in the present embodiment it wasarranged that the areas for acquiring the spare images do not overlapwith that for acquiring an image where the roughness analysis isperformed, both areas may coincide. However, note that when both do notcoincide, there is an advantage that damage caused by the electron beamirradiation to the specimen will be reduced. While in the presentembodiment the number of set examination areas was illustrated as 4, itmay generally be more or less than 4. Note that the number ofexamination areas increases, the accuracy of A to be calculatedimproves. In order to calculate A accurately, image data acquired at asfine sampling intervals as possible is used preferably. Thus, as thespare images, images acquired under higher magnification conditions thanthe images for roughness analysis are used preferably.

When the processor user inputs the number of set areas for determiningA, rectangles corresponding in number to the set areas are displayedsuperimposed on a CAD image displayed on CAD data display 2201 (seeareas 1–4 of FIG. 22). A y-direction length Ln of each area and a lengthobtained by dividing the y-direction length of the visual filed of thedisplayed CAD image evenly by the number of set areas are default set.Argument n for L is one of natural numbers 1–4 corresponding to areas1–4 in the present embodiment. Similarly, even in the x-direction, adefault-set length is allocated to a line-edge on the CAD image. Whilethe y-direction lengths of the respective area are set to the samelength in default, but may be set to ones changing depending on thehistories of the wafers examined. In this case, the processor usermanipulates a pointer indicated by an arrow in FIG. 21, thereby changingthe size of each of areas 1–4. When setting of each area is terminated,the processor user sets a sampling interval. In FIG. 22, the samesampling interval of 1.0 nm is set for areas 1–4, but the samplinginterval may be changed for each area. When all the parameters have beenset, the user clicks ENTER button 2308, thereby terminating inputtingdata to the set picture of FIG. 22. In order to operate the systemactually, other conditions including ones for setting the optoelectronicsystem need be set, but their description will be omitted in theembodiment. Actually, the other conditions are set using a separatesetting picture different from that of FIG. 21.

When ENTER button 2208 is clicked, wafer 2003 is placed on the stagewithin SEM housing 2001, thereby acquiring an actual image of an area ofthe wafer corresponding to the CAD image shown in FIG. 22. In order toacquire the image, a logic address on the CAD data need align with aphysical address on the wafer, but its description will be omitted. Eachof areas 1–4 where the image data were acquired in this process is 400pixels long by 100 pixel across with one side of a pixel being 7.5 nm,as set in FIG. 21.

Image data for setting parameter A was acquired for each of areas 1–4set in FIG. 22. By changing averaging parameter S in the verticaldirection of the image sequentially from 3 to 15, edge roughness indexesσ_(Am) (S) were calculated. These results were fitted using Ex. 9, orthe fourth method, and then the values of A were calculated. To thisend, the values of A were calculated for the four respective set areas1–4 and their averaged value was employed newly as A, which was 5.2 nm.This value of A was then stored in the storage of information processor2006 and also captured into the examination recipe corresponding to theexamination specimen. Note that when a previous calculated A value canbe used in the roughness analysis, the step of acquiring the spareimages is may be omitted.

When the process for calculating A is terminated, the picture returns toa state of FIG. 21 on which 5.2, or the value of A acquired, isdisplayed on cell 2109. Then, length L in the y-direction of theexamination area and a data sampling interval within length L are set.

Then, an image acquiring process is performed in a place where thelength measurement is actually performed under the conditions of FIG.21. Auto focus is performed on the length measurement area set in theexamination recipe. Then, the area is irradiated with an electron beamand secondary electron image data is acquired from the area set in FIG.21. The acquired image data comprises an averaged value of secondaryelectron signal intensities obtained in 16 scanning operations eachperformed from the upper left corner to the lower right corner of thevisual field. The reason that the number of scanning operations was 16is to reduce damage to the observation pattern. However, all the more,noise occurring in the observation image increased.

When the image of the area whose length was measured has been acquired,the analysis flow of FIG. 11 starts. The analysis mainly comprises step1102 that obtains a dependability of roughness index σ_(m) obtained fromthe observation image on the averaging parameter S, and step 1103 thatfits the dependability and calculates contribution σ₀ of roughnesspresent in the pattern, and a roughness index bias value σ_(e) based onthe influence of random noise. Since steps 1101 and 1102 were explainedwith reference to Embodiment 4, further description thereof will beomitted in this embodiment.

When up to step 1102 have been terminated, a data series {(S_(i), σ_(m)(S_(i))}: {(S_(min), σ_(m) (S_(min))}, {(S_(min)+1), σ_(m) (S_(min)+1)},. . . , {(S_(max), σ_(m) (S_(max))} to calculate σ₀ and σ_(e) isobtained. In step 1103, fitting is actually performed using the dataseries {(S_(i), σ_(m) (S_(i))}. Step 1103 will be next described indetail using FIG. 17.

First in step 1701, the data series {(S_(min), σ_(m)(S_(min))}:{(S_(min)+1), σ_(m) (S_(min)+1)}, . . . , {(S_(max), σ_(m) (S_(max))}thus obtained is displayed as a graph on monitor 2007.

Then in step 1702, fitting is performed by information processing means2006 according to Ex. 9 using the value of A, 5.2, registered in theexamination recipe corresponding to the wafer now under examination. Thefitting parameters are two: σ₀ and σ_(e) (1). As an algorithm forfitting purposes, the least squares method is used, thereby calculatingthose parameter values best describing σ_(m)(S) obtained from theobservation image. In this case, σ_(e) (1) was used as σ_(e). In thepresent embodiment, σ₀=2.25 nm and σ_(e)=0.95 nm were obtained. Theresults were displayed on the monitor picture and stored along withtheir identification codes to be used for registration in the storage ofinformation processing means 2006. As the identification codes,identifiers corresponding to the wafers and examination places, a datewhen the roughness analysis (or image acquisition) was performed, or theuser's peculiar management codes may be used.

Thus, the process of FIG. 11 was terminated and σ₀ and σ_(e) wereobtained. The σ₀ was used as an index representing a merit of the shapeof the observation pattern and the σ₀ was recorded as an indexindicative of a degree of noise involving the examining device. Sincethese two parameters can be obtained accurately and rapidly, theefficiency of pattern shape management and the productivity improved. Inaddition, the performance of the examination device can be monitoredover a long time and hence productivity improved.

While in the present embodiment method 5-2 was used as the algorithmthat performed the roughness analysis, another algorithm may beselected. In this case, the methods 5-1 to 5-3 are preferably set on theexamination recipe such that the processor user can select one of themethods 5-1 to 5-3. For example, use of Ex. 11 instead of Ex. 9 in thefitting in step 1103 will lead to calculation of σ₀ and σ_(e) in method5-1. Use of Ex. 12 before the process of obtaining A and Ex. 13 in thefitting of step 1103 will lead to calculation of σ₀ and σ_(e) in method5-3. Since the same data series {(S_(i), σ_(m) (S_(i))} is used evenwhen any of those methods is used, implementation of this function isachieved only by correcting the software.

While in the present embodiment the set of image data in the area pickedup when the parameter A was determined was used as it is as the set ofimage data in the place where the roughness analysis was performed, itis possible to newly pick up an image whose roughness analysis is to beperformed. In that case, it is possible to use a different algorithm forthe roughness analysis depending on the image pickup magnification. Forexample, a dialog box that specifies a place where the lengthmeasurement is actually made may be provided on the GUI picture of FIG.21 such that the size of the image pickup area or the scanning area canbe set on the GUI picture of FIG. 21. In this case, the algorithm forsetting parameter A and the algorithm for performing the roughnessanalysis are provided separately. For example, the algorithm of method5-2 is preferable for analysis of a low magnification image while method4 is preferable for analysis of a picked-up image of a relatively highmagnification. Thus, the arrangement may be such that a lowmagnification image of a relatively wide range is analyzed in method5-2, thereby determining parameter A, a higher magnification image foranalysis is acquired, and then roughness analysis is performed on theacquired image using the algorithm of method 4, thereby improving theanalysis accuracy compared to the analysis using the same algorithm.

While in the present embodiment the edge roughness was calculated, theline width roughness may be used as an index instead of the line-edgeroughness as in Embodiments 3 and 4. While in the present embodiment thein-line measurement was described, this method is applicable to theoff-line measurement, of course. In the off-line measurement, the imageof the examination area acquired is stored along with an appropriateimage managing identifier, for example, a wafer identifier andcoordinate information on the image pickup area in the informationstorage means. In the roughness analysis, the image data set is calledand analyzed as requested. While in the present embodiment theexamination area is illustrated as specified using a CAD image, theexamination area may be specified with a real image. For example, alow-magnification wide-range real image can be acquired and displayed onthe recipe setting picture of FIG. 21 or 22 and then a rectangularfigure may be displayed superimposed thereon for area setting purposes.

Since the roughness analysis method described in the present embodimentdoes not involve Fourier's spectrum, calculation is simple and not timeconsuming. In addition, since a contribution to roughness of the highfrequency components that cannot be detected due to noise reduction hasbeen corrected accurately, the roughness analysis method ensure highanalysis accuracy.

(Embodiment 6)

It is possible to predict results measured at different samplingintervals, using the results of measurement obtained in Embodiment 5.The present embodiment shows an example of calculation of a value of σ₀which will be obtained when measured at smaller sampling intervalssubsequent to the measurement made in Embodiment 5.

A value of 2.25 nm indicative of σ₀ obtained in Embodiment 5 correspondsto real dispersion of edge point positions obtained when a 200-nm-longline-edge was edge detected with an interval of 7.5 nm. However,evaluation of the influence of the accuracy on the device performancedemands a roughness value corresponding to a sampling interval of 2 nm.Thus, σ₀ corresponding to the sampling interval of 2 nm was calculatedaccording to the following procedures.

First, the value of A obtained from σ_(A)=1.25 nm is calculated inaccordance with Ex. 9. More specifically, the user calls a predictionprogram from information processor 2006 through monitor 2007 andinformation input means 2008. When the program is called, a request toinput a retrieval key to thereby call a result of the roughness analysisis displayed on monitor 2007. The user inputs the retrieval keyaccordingly. One of various identification codes described withreference to Embodiment 5 may be used as the retrieval key. Theroughness analysis program may be arranged such that the roughnessanalysis result may be called on the examination recipe. When theretrieval key is inputted, the values of σ_(e) already calculated as σ₀is loaded on the memory of information processor 2006. A request toinput f₀, S₀ and Δy is displayed on monitor 2007. The device user inputs1/f₀=2000 nm, S₀=3 and Δy=0.75 nm according to the request. Then, thevalue of A is calculated according to Ex. 9. Then, Ex. 4 is integratedfrom f₁ to f₂ where f₁=1/2Δy and f₂=1/(2·2), using the value of Aobtained. As a result, an evaluated value of A was 0.009 nm². From theabove, a dispersion value obtained when the edge of 2000 nm was sampledat intervals of 2 nm was 2.25²+0.009² and σ₀ was obtained as the squareroot of this value. Since the significant figures were 0.01 nm, σ₀obtained when the edge was sampled at intervals of 2 nm was 2.25 nm,which was the same value as that obtained when sampled at intervals of7.5 nm.

As described above, a combination of the fifth method and the results ofhigh and low magnification observations enables a value of edgeroughness obtained by sampling the long line-edge at very fine intervalsto be free from the influence of noise.

The high-accuracy pattern shape evaluating method and apparatusaccording to the present invention quantifies the influence of randomnoise due to the observation device included in line-edge roughnessobtained from a pattern image in the examination process of asemiconductor manufacture and subtracts this quantified influence fromthe measured value, thereby enabling a value of roughness present in thepattern to be obtained with high accuracy. Thus, high-accuracyexamination is achieved and productivity improves.

Since the influence of random noise arising from the observation deviceon the image is quantified, the observation requirements can bedetermined using this value. In addition, by managing this value over along time, long time stability of the apparatus performance can beevaluated. Thus, the accuracy of the examination and productivityimprove.

It should be further understood by those skilled in the art thatalthough the foregoing description has been made on embodiments of theinvention, the invention is not limited thereto and various changes andmodifications may be made without departing from the spirit of theinvention and the scope of the appended claims.

1. A pattern shape evaluating apparatus comprising: a scanning electronmicroscope for acquiring an electron beam image of an examinationspecimen with a formed line pattern; an information processing devicefor processing the electron beam image acquired by the microscope;information input means for inputting required information to theinformation processor, and storage means for storing first image datanecessary for performing a compensation operation; wherein theinformation processor: acquires a plurality of position coordinates ofend points of the line pattern along the line pattern from image data ina predetermined area of the line pattern; performs an averaging processany number of times on a roughness data series formed by differenceseach between a respective one of the acquired position coordinates andan average value of the position coordinates; calculates a standarddeviation of the roughness data series subjected to the averagingprocess, using the real value and bias component of roughness as fittingparameters to the standard deviation, thereby producing a data series ofstandard deviation for the number of times of performing the averagingprocess; calculates a real value and bias component of roughnessincluded in the edge roughness index, using the standard deviation dataseries; displays on the monitor a request to input a minimum and amaximum value of the number of times of performing the averagingprocess; repeats the averaging process the number of times correspondingto the maximum of the number of times of performing the averagingprocess inputted by the information inputting means; and displays on themonitor an image involving the first image data and a request to selecta predetermined area of the image.
 2. The pattern shape evaluatingapparatus of claim 1, further comprising: a monitor for displaying thereal value and bias component of roughness thereon.
 3. The pattern shapeevaluating apparatus of claim 1, wherein: the information processorperforms a compensating operation including compensating the data seriesof standard deviation involving the number of times of performing theaveraging process for components of the data series missing due to theaveraging process.
 4. The pattern shape evaluating apparatus of claim 1,wherein: the storage means stores second image data of an examinationarea acquired at a higher magnification than the first image data; andthe information processor performs the compensating operation on thedata series of standard deviations formed from the second image data,using the parameters calculated based on the first image data.
 5. Thepattern shape evaluating apparatus of claim 1, wherein: the informationprocessor performs the compensating operation on a further part of thefirst image data stored in the storage means.
 6. The pattern shapeevaluating apparatus of claim 3, wherein: the information processor hasstored a plurality of different compensation algorithms each selectableby the user; and calculates parameters to be used for the compensatingoperation, using image data of the predetermined area selected accordingto the request for selection.
 7. The pattern shape evaluating apparatusof claim 3, wherein; the monitor displays CAD data corresponding to thepredetermined area as the first image data.